Failing that, I could fake some additional symptoms and get see as an emergency
Good luck with that. Getting seen by a halfway decent doctor when you are a genuine emergency is hard enough.
If I were you I'd be heading to the nearest private clinic (Medicover have one in Gdansk I think). Private medical cover is a damn good idea here and not hugely expensive, Medicover starts at 95zl per month, which is the same as a couple of beers a week.